Rule: Q[3, 4, 22]

Type

Polynomials

One starts from the polynomial $P_1$ and extends one by one with $P_{\mathrm{i}}$ until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

• $P_1$:
  $\frac{5}{2}\cdot t^3-\frac{3}{2}\cdot t$
• $P_2$:
  $\frac{5}{2}\cdot t^7-\frac{77}{18}\cdot t^5+\frac{3745}{1782}\cdot t^3-\frac{155}{594}\cdot t$
• $P_3$:
  $\frac{5}{2}\cdot t^{29}-\frac{743669323805712117007731327878993851}{40447298096103332088703889100919674}\cdot t^{27}+\frac{1046521699784301611483166275920753859533268}{17233764549138659684688908716175304238083}\cdot t^{25}-\frac{110664717568165749909700048133151577106772475}{930623285653487622973201070673466428856482}\cdot t^{23}+\frac{2747084854810141283411788463274164152221975250}{17893347719610239296257456949767104518467813}\cdot t^{21}-\frac{265056795145182933462025686099787279913766800}{1928355769281303984308447741453597730060441}\cdot t^{19}+\frac{38706809713354030801169566531204646635001585}{442927655689263100037234495235840374971866}\cdot t^{17}-\frac{184756818941865306873002442113148675307520395}{4650740384737262550390962199976323937204593}\cdot t^{15}+\frac{1471675042226378965268664210019967970998288675}{114718262823519142909643734266082657117713294}\cdot t^{13}-\frac{2316317979591846517471666712480217465869902375}{803027839764634000367506139862578599823993058}\cdot t^{11}+\frac{524422897773363417790480402275496825177546375}{1204541759646951000551259209793867899735989587}\cdot t^9-\frac{344423095571031379049676541627091048068861195}{8297954344234551337130896778579978864847928266}\cdot t^7+\frac{4009859877375307622748440000949070455336385}{1778133073764546715099477881124281185324556057}\cdot t^5-\frac{4349927535939151271426789802524855111909975}{75443646129724339197792132956273073148770449847}\cdot t^3+\frac{717087770813170603392101032369283870075}{1622444002789770735436389956048883293521945158}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Legendre type can be downloaded here packed into a single file.